Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1]. - Open Research Data - MOST Wiedzy

Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].

Description

The presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.

The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses travelling-wave solutions that are positive and bounded. Moreover, such solutions are spatially monotone at each instant of time, and temporally monotone at each spatial point. Unfortunately, only a few travelling-wave solutions of such model are known in exact form, therefore, the construction of a suitable numerical method is highly desirable.

The complete convergence analysis of the constructed nonstandard difference scheme is available in the paper: On the convergence of a finite-difference discretization a la Mickens of the generalized Burgers–Huxley equation (2014) Vol. 20, No. 10, 1444–1451, http://dx.doi.org/10.1080/10236198.2014.936319.

We provide nonstandard approximation of the travelling wave solution bounded within [0,1]. The dataset consists of text files (.txt) with simulation results which contain the maximum-norm errors. Results are obtained for couple of sets of model parameters:  α, γ, p and the space interval [-20,20]. Time interval is set to be [0,20]. Each file contains six results for different combination of time and space steps which satisfy the convergence conditions derived in the above paper.

1. α = 1, γ = 0.8, p = 2 – [0,1]solution1.txt
2. α = 1, γ = 0.7, p = 2 – [0,1]solution2.txt
3. α = 1, γ = 0.6, p = 2 – [0,1]solution3.txt
4. α = 1, γ = 0.8, p = 1 – [0,1]solution4.txt
5. α = 1, γ = 0.7, p = 1 – [0,1]solution5.txt
6. α = 1, γ = 0.6, p = 1 – [0,1]solution6.txt
7. α = 0.8, γ = 0.8, p = 1 – [0,1]solution7.txt
8. α = 0.6, γ = 0.8, p = 1 – [0,1]solution8.txt
9. α = 0.8, γ = 0.8, p = 2 – [0,1]solution9.txt
10. α = 0.6, γ = 0.8, p = 2 – [0,1]solution10.txt

Dataset file

MaximumNormErrors[0,1]Solution.zip

Details

Year of publication:
2020
Dataset language:
English
Fields of science:
• Mathematics (Natural sciences)